The Cyclizer Function on Permutation Groups
نویسندگان
چکیده
Let G be a transitive permutation group acting on a finite set Ω. A cycle c is involved in a permutation g if and only if gc−1 fixes all points of Supp(c). We define a function Cyc(G) which takes the permutation group G to the group generated by the cycles involved in its elements. Let Cyc1(G) = Cyc(G) and Cyci+1(G) = Cyc(Cyci(G))). It is known that Cyc3(G) = Cyc4(G) for all such groups. We investigate and characterize those groups for which Cyc2(G) 6= Cyc3(G).
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